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lassical Physics II
Classical Physics II
PHY132
Lecture 17
Induction
Lecture 16
1
03/08/2010

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*Sign up*Ampere’s Law
the Biot-Savart Law (infinitesimally small current wire segment, or
speeding charge) has a
1/
r
2
form,
– it leads to a
1/
r
form for the field of an infinitely long wire,
nd o a constant field for a infinitely large “sheet” of current
arrying wires
– and to a constant field for a infinitely large
sheet of current-carrying wires…
This leads to a “geometric” interpretation of the field: field lines!
The magnetic field lines always form closed loops
– because of Gauss’ Law for magnetism, or the absence of magnetic monopoles …
Above two observations results in AMPERE’S LAW, which (like Gauss’
Law for Electrostatics) is very useful for finding the B-field in
symmetric situations.
– Ampere’s Law is derivable as an (
line
) integral form of the Biot-Savart Law…
Ampere’s Law:
e
n
c
l
o
s
e
d
dI
Bs
–wh
e
r
e
I
enclosed
is a current flowing through the surface enclosed by the curve,
ore specifically:
0e
closed
curve
Ampere's Law
Lecture 16
2
more specifically:
03/08/2010
enclosed
surface area bounded
by the closed curve
I
d
j
A

Applying Ampere’s Law
Ampere’s Law is utilized by computer programs for field
calculations.
or ur purposes it is mostly useful in symmetric situations
For our purposes it is mostly useful in symmetric situations
– e.g. a long straight wire with current
I
(into the paper):
– the B-field lines are circles around the wire:
– Ampere’s Law applied to the dashed circle:
B
r
I
d
Bs
2
B
r
2
r
B
ds
circle
radius
r
0e
n
c
l
o
s
e
d
0
II
0
–
s we found before
0
2
I
B
r
Lecture 16
3
as we found before!
03/08/2010

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*Sign up*Magnetic Field from a Solenoid
We’ll now use Ampere’s Law for other symmetric situations:
The field of a very long solenoid:
–
mpere’s Law applied to the
Rectangular
Amperian Loop
l
Ampere s Law applied to the
dashed rectangle:
•t
h
e
B
·
d
l
vanishes
for the left & right
f
fg
sides because
B
is
(nearly) perpendicular
to these sides
he
B
·
d
l
vanishes
for the top side
because
B
is (nearly) zero there…
hus:
I
N windings
enclosed by the
rectangle
– Thus:
rectangle
d
Bs
0 enclosed
I
0
NI
0
eal solenoid
NI
B
l
sol
B l
Lecture 16
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ideal solenoid